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问题描述

　　已知一个有理数类Zrf_Ratio，实现如下的操作符重载形式：
　　friend std::ostream& operator<<(std::ostream&, const zrf_Ratio&);//输出最简分数
　　friend std::istream& operator>>(std::istream&, zrf_Ratio&);
　　friend bool operator==(const zrf_Ratio&, const zrf_Ratio&);
　　friend bool operator<(const zrf_Ratio&, const zrf_Ratio&);

测试

　　测试时主程序会输入四个整数a, b, c, d，表示两个分数a/b和c/d。要求输出最简分数以及两个分数相等和大小的比较结果。

样例输入

1 7 26 25

样例输出

zrf is:1/7; ssh is:26/25
(zrf==ssh) is:0; (zrf<ssh) is:1

ostream& operator<<(ostream& os, const zrf_Ratio& zrf_Ratio){

	os << zrf_Ratio.num << "/" << zrf_Ratio.den;

	return os;

}

istream& operator>>(istream& in, zrf_Ratio& zrf_Ratio){

	in >> zrf_Ratio.num >> zrf_Ratio.den;

	return in;

}

bool operator==(const zrf_Ratio& z1, const zrf_Ratio& z2){

	if(z1.num == z2.num && z1.den == z2.den)

		return true;

	return false;

}

bool operator<(const zrf_Ratio& z1, const zrf_Ratio& z2){

	if(z1.num * z2.den < z2.num * z1.den)

		return true;

	return false;

}

#include <iostream>

#include <cassert>

using namespace std;

class zrf_Ratio

{

     friend std::ostream& operator<<(std::ostream&, const zrf_Ratio&);

     friend std::istream& operator>>(std::istream&, zrf_Ratio&);

     friend bool operator==(const zrf_Ratio&, const zrf_Ratio&);

     friend bool operator<(const zrf_Ratio&, const zrf_Ratio&);

public:

     zrf_Ratio(int=0,int=1);

     zrf_Ratio(const zrf_Ratio&);

private:

     int num;

     int den;

     void reduce();//化为最简分数

};

//补充函数：

ostream& operator<<(ostream& os, const zrf_Ratio& zrf_Ratio){

	os << zrf_Ratio.num << "/" << zrf_Ratio.den;

	return os;

}

istream& operator>>(istream& in, zrf_Ratio& zrf_Ratio){

	in >> zrf_Ratio.num >> zrf_Ratio.den;

	return in;

}

bool operator==(const zrf_Ratio& z1, const zrf_Ratio& z2){

	if(z1.num == z2.num && z1.den == z2.den)

		return true;

	return false;

}

bool operator<(const zrf_Ratio& z1, const zrf_Ratio& z2){

	if(z1.num * z2.den < z2.num * z1.den)

		return true;

	return false;

}

//公有成员函数:

zrf_Ratio::zrf_Ratio(int num, int den) : num(num), den(den)

{

     reduce();

}

zrf_Ratio::zrf_Ratio(const zrf_Ratio& r) : num(r.num), den(r.den)

{

}

//私有成员函数:

void swap(int &m, int &n)

{

     int t;

     t=m;

     m=n;

     n=t;

}

int zrf_Gcd(int m, int n)

{

     if (m<n)

         swap(m,n);

     assert(n>=0);

     while (n>0)

     {

         int r=m%n;

         m = n;

         n = r;

     }

     return m;

}

void zrf_Ratio::reduce()

{

     if (num == 0 || den == 0)

     {

         num = 0;

         den = 1;

         return;

     }

     if (den < 0)

     {

         den *= -1;

         num *= -1;

     }

     if (num == 1)

         return;

     int sgn = (num<0?-1:1);

     int g = zrf_Gcd(sgn*num,den);

     num /= g;

     den /= g;

}

int main()

{

     int a = 0, b = 0, c = 0, d = 0;

     cin >> a >> b >> c >> d;

     zrf_Ratio zrf(a, b),ssh(c, d);

     std::cout<<"zrf is:"<<zrf<<"; ssh is:"<<ssh<<'\n' ;

     std::cout<<"(zrf==ssh) is:"<<(zrf==ssh)<<"; (zrf<ssh) is:"<<(zrf<ssh) <<endl;

     return 0;

}